Method for performing transformations of color data

Abstract

The invention includes a method for the computer-aided performance of color space transformations with high accuracy that provides a result which is as close as possible to the original. The source color space includes n colors, the target color space includes m values, and combinations of the m components of the target color space are assigned to at least some combinations of the n colors of the source color space via the transformation rule TRV.

Claims

1. Method for computer-aided execution of transformations of color data from a source color space to a target color space using a transformation rule TRV, wherein the source color space comprises n colors, which are present in combinations of color components q(1) to q(n) in each point to be represented, the target color space comprises m values that can be combined to form combinations of components z(1) to z(m), combinations of them components of the target color space are assigned to at least some combinations of the n colors of the source color space via the transformation rule TRV, characterized by the following steps: a) for a combination KB of the n colors of the source color space with color components q.sup.KB (1) to q.sup.KB (n) for which no combination of the m components z.sup.KB (1) to z.sup.KB (m) of the target color space is assigned via the TRV, select a color i of the combination KB which has a color component FA=q.sup.KB (i)>0 and for which the following conditions apply: i) the remaining combination of color components q.sup.KB (j not equal to i) without the component of color i is assigned a combination of the target color space with components z(1).sup.i, z(2).sup.i, . . . , z(m).sup.i, and ii) two further, with one exception mutually identical combinations of color components q(1) to q(n) exist, to each of which a combination of components z(1) to z(m) is assigned and wherein the two combinations of color components q(1).sup.1 to q(n).sup.1 and q(1).sup.2 to q(n).sup.2 differ only in that the color component q(i) of color i in the one q(i).sup.1=FA>0 and in the other q(i).sup.2=0, so that 1) The combination q(1).sup.1 to q(n).sup.1 with color component q(i).sup.1=FA is assigned a corresponding combination of the components z(1).sup.1, z(2).sup.1, . . . , z(m).sup.1 of the m values of the target color space, which forms the color data set Z1, and 2) the combination q(1).sup.2 to q(n).sup.2 with color component q(i).sup.2=0 is assigned a corresponding combination of the components z(1).sup.2, z(2).sup.2, . . . , z(m).sup.2 of the m values of the target color space, which forms the color data set Z2, iii) Calculating the ratios V(1).sup.i, V(2).sup.i, . . . , V(m).sup.i of each component z(1).sup.1, z(2).sup.1, . . . , z(m).sup.1 of the m values of the color data set Z1 to the respective component z(1).sup.2, z(2).sup.2, . . . , z(m).sup.2 of the m values of the color data set Z2, which form a set of factors V(1).sup.i=z(1).sup.1/z(1).sup.2, V(2).sup.i=z(2)/z(2).sup.12, . . . , V(m).sup.i=z(m)/z(m).sup.12, b) Applying the factors V(1).sup.i, V(2).sup.i, . . . , V(m).sup.i for transformations of combinations KB of colors of the source color space with n colors, which contain the color component FA of color i, but for which the color component q(i)=0 is set for the transformation, into the target color space with m components by multiplying the z(1).sup.i, z(2).sup.i, . . . , z(m) of the target color space resulting from the transformation by the respective factors V(1), V(2), . . . , V(m), z(m).sup.i of the target color space are multiplied by the respective factors V(1).sup.i, V(2).sup.i, . . . , V(m).sup.i.

2. The method according to claim 1, characterized in that the method is applied to partial combinations of k<n colors for a given combination of then colors with combinations of color proportions q(1) to q(n).

3. The method according to claim 2, characterized in that the method is applied to successive partial combinations with k<n colors up to k=n, the resulting factors being applied multiplicatively.

4. Method according to claim 1, characterized in that the size of the color portion of a color is taken into account for achieving a higher accuracy by preferentially selecting from the possible colors i the one with smaller color portion.

5. Method according to claim 1, characterized in that for several different possible colors i1, i2, . . . the results of the different estimates z(1).sup.i1, . . . , z(m).sup.i1 as well as z(1).sup.i2, . . . , z(m).sup.i2 etc. are averaged in a weighted manner, the weight of each estimate being selected to be greater the smaller the respective color proportion q(i1), q(i2), . . . of the color.

6. Method according to claim 1, characterized in that the components z(1) to z(m) of the target color space are device-dependent values.

7. Method according to claim 1, characterized in that the components z(1) to z(m) of the target color space are device-independent values.

8. Method according to claim 1, characterized in that the transformation rule TRV is in the form of transformation tables.

9. Method according to claim 1, characterized in that the method is carried out on a computer unit by means of control software, the computer unit comprising an input unit for providing the digital color data of the source color space of the project and an output unit for outputting the transformed values of the target color space as well as a memory on which transformation tables are stored, values for the target color space being generated for the color data of the source color space of the project by means of the control software using the transformation tables and applying the method according to claims 1 to 8 and being provided in a data set.

Description

(1) Based on the prior art described above, the invention is based on the task of improving a method for performing color space transformations using transformation rules in such a way that even combinations of color data from the n colors of the source color space, which include both components or subgroups for which transformation tables are available and those for which no transformation tables are available, can be transformed with high accuracy into the m values of the target color space in such a way that a result that comes as close as possible to the original can be achieved.

(2) The technical solution to this task consists in a method with the features of patent claim 1. Further advantages and features result from the subclaims.

(3) The invention provides a fast estimation method that assembles mixtures from known subcomponents. For example, if the input asks for a mixture CMYKO, but only interpolation tables or ICC color profiles for CMYK as well as for OMYK are available, the entries are cleverly combined.

(4) According to the invention, a method is proposed for performing transformations of color data from a source color space with n colors into a target color space with m values using a transformation rule TRV, where a color i is one of the n colors of the source color space and the color components of the colors q(1), q(2), . . . , q(n) are assigned values z(1), z(2), . . . , z(m) of the target color space at least for some combinations of the n colors of the source color space, characterized by the following steps: a) for a combination KB of the n colors of the source color space with color components q.sup.KB (1) to q.sup.KB (n) for which no combination of the m components z.sup.KB (1) to z.sup.KB (m) of the target color space is assigned via the TRV, select a color i of the combination KB which has a color component FA=q.sup.KB (i)>0 and for which the following conditions apply: i) the remaining combination of color components q.sup.KB (j not equal to i) without the component of color i is assigned a combination of the target color space with components z(1).sup.i, z(2).sup.i, . . . , z(m).sup.i, and ii) two further, with one exception mutually identical combinations of color components q(1) to q(n) exist, to each of which a combination of components z(1) to z(m) is assigned and wherein the two combinations of color components q(1).sup.1 to q(n).sup.1 and q(1).sup.2 to q(n).sup.2 differ only in that the color component q(i) of color i in the one q(i).sup.1=FA>0 and in the other q(i).sup.2=0, so that 1) the combination q(1).sup.1 to q(n).sup.1 with color component q(i).sup.1=FA is assigned a corresponding combination of the components z(1).sup.1, z(2).sup.1, . . . , z(m).sup.1 of the m values of the target color space, which forms the color data set Z1, and 2) the combination q(1).sup.2 to q(n.sup.) 2 with color component q(i).sup.2=0 is assigned a corresponding combination of the components z(1).sup.2, z(2).sup.2, . . . , z(m).sup.2 of the m values of the target color space, which forms the color data set Z2, iii) Calculating the ratios V(1).sup.i, V(2).sup.i, . . . , V(m).sup.i of each component z(1.sup.) 1, z(2).sup.1, . . . , z(m).sup.1 of the m values of the color data set Z1 to the respective component z(1).sup.2, z(2).sup.2, . . . , z(m).sup.2 of the m values of the color data set Z2, which form a set of factors V(1).sup.i=z(1).sup.1/z(1.sup.) 2 V(2).sup.i=z(2)/z(2).sup.12, . . . , V(m).sup.i=z(m)/z(m).sup.12, b) Applying the factors V(1).sup.i, V(2).sup.i, . . . , V(m).sup.i for transformations of combinations KB of colors of the source color space with n colors, which contain the color component FA of color i, but for which the color component q(i)=0 is set for the transformation, into the target color space with m components by multiplying the z(1).sup.i, z(2).sup.i, . . . , z(m) of the target color space resulting from the transformation by the respective factors V(1), V(2), . . . , V(m), z(m).sup.i of the target color space are multiplied by the respective factors V(1).sup.i, V(2).sup.i, . . . , V(m).sup.i.

(5) The underlying idea is to construct the output values for an unknown input combination step by step from the output values of known input combinations, estimating at each step the color impact (on the output values) of added input colors and adding this contribution in a way that is detailed below.

(6) In a known input color combination, i.e. for which output color values are available, e.g. by table or interpolation, the sought contribution of partial colors within this color combination is determined as follows. The input combination AB is decomposed into the contribution of the partial colors A and the contribution of the remaining colors B, with the aim of describing the color effect of A relative to the base B, so that it can then be applied to another base C to estimate an unknown combination AC.

(7) In the approach proposed here, the blend AB is considered as an overlay of two layers A and B and the established blending modes of computer graphics are used (W3C, PDF, Photoshop). The most important blending mode is Multiply. It is based on linear color values, in this case linear values, normalized between 0 and 1. Multiply multiplies the linear values of two layers in a light-related color space (in computer graphics this is often RGB) to simulate the darkening, inking overlay of the colors. The effect is similar to an overprint.

(8) Then applies: Linear values of the mixture AB=(linear values of A)*(linear values of B). After the searched colored contribution of A, thus the factor linear values of A, can be solved. The linear values of AB and B are both known from the table containing AB. In an optical analogy, the linear values of A behave like a transmission factor of the added colors, applied to the linear values of the base B.

(9) For linear light-related target color spaces such as CIEXYZ and reflectance spectra, their output values can be taken directly as linear values; for CIELAB, they are first converted to CIEXYZ, calculated in CIEXYZ, and converted back at the end of the calculations.

(10) For nonlinear RGB target color spaces, calculations are performed in their linearized domains, e.g. in the case of gamma-based RGB color spaces with values from 0 to 1, the nonlinearity is removed by exponentiation with gamma, the RGB linear values linearized in this way are used, and finally one returns to the nonlinear RGB space by exponentiation with 1/gamma.

(11) In an ink-related target color space, the print color values x between 0-100% are inverted to their complementary values (1?x) and linearized analogously to the RGB case and de-linearized again after the offset. These complementary values are the linear values for Multiply. The calculation with print color values thus corresponds formulaically to the Blending Mode Screen, also called inverse multiply. This follows the usual processing in PDF for RGB or DeviceCMYK (Adobe, PDF Blend Modes, Addendum to PDF Reference 5th edition, version 1.6, 2006, p. 2, p. 6). The complementary values again behave like transmission factors, and the ink contributions themselves therefore like absorptions.

(12) This approach is similar to the well-known concept of the ink acceptance formula in printing according to Preucil, in which the linear color values, here the reflectance values, of the ink B printed first and the ink A printed on top are measured individually as well as in the combined print AB, and the latter measurement is approximated with the product approach AB?A.sup.fa*B, here to determine the unknown ink acceptance factor fa, which modifies A by a mostly reduced film thickness <1. In contrast, the invention uses the known linear values of AB and B to determine the color effect of A from the AB=A*B approach.

(13) Herein is proposed a method to determine the color effect of some colors A within a known combination AB and apply it to other colors C to estimate the output values for a combinations AC.

(14) In the simplest form, one can describe separately for each input color its effect on the substrate by comparing the output values of the input color value with the output values of the substrate (input color value zero). The difference in the output values is a measure of the color effect of the input color in its quantity described by the value. All these effects are then added together.

(15) However, the further proposal according to the invention significantly improves the estimation of a color combination by adding individual inks to the substrate step by step by proceeding in printing sequence, i.e., as the individual inks are applied to the substrate one after the other, and taking into account process-typical ink acceptance properties, which are known to be about 75% for wet-on-wet overprinting of solids in offset printing, for example, by correcting the transmission factors, i.e., the linear values, exponentially with the ink acceptance.

(16) If, on the other hand, not only single colors but also color combinations in subspace tables are known, it is better, according to a suggestion in accordance with the invention, to read off the interaction of a group of as many partial colors of the input combination as possible directly from existing tables as known output values instead of estimating it from single colors. At the beginning, one selects a group of colors for which a subspace table is available, for example in such a way that its input color values already cover as large a proportion as possible of the entire input combination. Then, from the remaining input colors, one identifies, for example, the one whose input color value has the largest share in the combination, and selects a subspace table that contains this color (ideally with a large overlap to the already known colors). For this subspace, one determines the color effect of this color by reading the output color values with this color as well as without this color and comparing them again. The difference is again a measure of what happens when this color is added to the given color value. So you apply this difference to the output values of the initial color group and thus you have added a color. This is the new initial combination for the next step, in which the next remaining color is identified and added until all the colors in the input combination are included.

(17) The method according to the invention is proposed generalized as follows:

(18) For a given input, color groups are searched for, for which a transformation is available, for example as a table, and which contain a part of the input combination. (The complete combination is not included, for it is to be estimated). This set of color groups is processed step by step. For example, one color group is selected as a starting point, and in the first step a second one is selected to be used to add an input color. In further steps more color groups are selected until all colors occurring in the input have been added.

(19) The following happens per step: First, the common printing colors (intersection) are identified from the color groups involved in the stepthis is at least two, at most the entire set. If there are no common inks, the intersection is the unprinted substrate, i.e. the zero entry in the table.

(20) Each color group of the step thus contains on the one hand the common printing inks, but also additional ones. For each color group, these additional, i.e. the non-common printing inks are identified.

(21) For each color group, the contained part of the input is considered as a mixture. The mixture is decomposed into the contribution of the common colors, which represents the base in the above calculation, and the contribution of the additional (added) colors. This gives a measure of their color effect (relative to the base).

(22) In this way, the color contribution of a color component A in a mixture AB relative to a base B is determined for each group in the target color space of the output colors. The crucial point is that this contribution can subsequently be applied to other bases, i.e. composed. Thus, for each color group involved, the contributions of the common colors as bases and the additional colors as complements are fixed. Now the contributions of the complements can be applied to the other color groups in this step. Thus one or more estimates are obtained for a previously unknown color mixture.

(23) If several decompositions have happened in a step and therefore alternative combinatorial ways of composition are possible, these are weighted and averaged to a final result of the step, where a useful weight is the relative certainty of the estimate (such as the distance from the partial results considered known). Below, an example explains that this increases the quality of color transition transformation results because jumps are avoided.

(24) A step is completed with the averaging. The final result of the step, as a newly generated color group now known through the estimation, is offset in the next step with further color groups, which in turn bring in further input colors, until finally the combination of all input colors is estimated. In this way, mixtures are composed step by step until the input is complete.

(25) Without further elaboration, it is believed that one skilled in the art can, using the preceding description, utilize the present invention to its fullest extent. The preceding preferred specific embodiments are, therefore, to be construed as merely illustrative, and not limitative of the remainder of the disclosure in any way whatsoever.

(26) In the foregoing and in the examples, all temperatures are set forth uncorrected in degrees Celsius and, all parts and percentages are by weight, unless otherwise indicated.

(27) The entire disclosures of all applications, patents and publications, cited herein and of corresponding European application No. 22020391.3, filed Aug. 15, 2022, are incorporated by reference herein.

(28) In the following example with the color groups CMYK and OMYK different strategies are shown, which represent different compromises between efficiency and accuracy. Further strategies are conceivable just because of the combinatorics of the decompositions, this execution is not limiting.

(29) The desired input is a color combination of CMYK+O with proportions of 30% C, 60% M, 10% Y, 20% K, 50% O. There are tables for CMYK and for MYKO, but no table for CMYKO. For simplification, it is assumed that the tables already contain light-related linear output values.

(30) The fastest way would be to use the first four colors, the CMYK color group, directly and only mix in the contribution of the missing colors (here only orange).

(31) So first the output values of the CMYK color group 30% C, 60% M, 10% Y, 20% K are read.

(32) The still missing color contribution of 50% O is determined in this way:

(33) The common colors of CMYK and MYKO are MYK. The additional color of CMYK is C, that of MYKO is O. MYK is taken as the base B with the values 60% M, 10% Y, 20% K, the output values are read off, and so are the output values of the mixture AB with the values 60% M, 10% Y, 20% K, 50% O. The output values of the mixture AB are read off. The transmission factor by which the addition of the color quantity A of 50% O changes the base is the quotient of the output values of AB and B.

(34) This factor is applied (multiplied) to the above reading of the output values of the CMYK color group 50% C, 60% M, 10% Y, 20% K and gives the desired result of the total CMYKO color values.

(35) The advantage of this method is that you can go sequentially from left to right without making any decisions, read off the first tabulated color value and apply all the colors still to be added further to the right as relative factors from their own tables (A=AB/B).

(36) An alternative is to use only the unprinted substrate instead of the common colors (here MYK) for B, then AB=A=the table value of 50% O, and the effect of 50% O is the quotient of the table value of 50% O and the table value of the unprinted paper.

(37) But you can imagine that an orange has a different effect on white paper than in the presence of many other colors. We are looking for the effect in the presence of 30+60+10+20% CMYK color quantity. This is unknown, there is no table for it. In order to estimate it realistically, it is obvious to use not the possibly strong effect of 50% O on paper, but the presumably different effect of 50% O on a 60+10+20% MYK color set.

(38) To increase accuracy, the size of the contributions to be added is considered. It is probably less accurate to add a large amount of paint 50% O than a smaller amount of paint 30% C. In other words, if one were to start with MYKO 60+10+20+50, one would already get 140% ink coverage as certain knowledge from the table, compared to only 120% ink coverage from CMYK 30+60+10+20 above. This improvement is bought with an additional sorting step.

(39) However, this size-dependent procedure then still contains a preferred order, which then becomes a problem when two values converge in a gradient. Let's assume that cyan would increase pixel by pixel from 30% to over 50%. The size-based sorting would choose MYKO as the base for the first pixels and add the smaller C value. Once C is equal to or minimally larger, the base would change to CMYK because now the O contribution is the smaller one. Generally, a jump occurs because the result from base CMYK+contribution 50% O is not equal to the result from base MYKO+contribution 50% C. This jump is an undesirable artifact.

(40) A further increase in quality would therefore use both combinations of base+contribution as described and average them weighted. Then the transition is guaranteed to be steady.

(41) A further example substantiates the process flow of the method according to the invention. The input color data are from a source color space with 4 color components q(1), q(2), q(3), q(4). These are to be transformed into a target color space with 3 color values z(1), z(2), z(3).

(42) The following transformation mappings are available for combinations of color components of the source color space: T(1) [q(1), q(2), q(3)], T(2) [q(1), q(2), q(4)], T(3) [q(1), q(3), q(4)], T(4) [q(2), q(3), q(4)], T(5) [q(3), q(4)].

(43) The input data set included the following values for q(1), q(2), q(3), q(4): 20406080

(44) First, a color i is to be selected. The necessary assignment conditions are fulfilled for all colors 1-4. Color 1 is chosen because its color component q(1) is the smallest and therefore a presumably smaller influence has to be estimated and will be applied to a large, known target color combination of the color components of colors 2-4.

(45) First, the combination of values Z.sup.i (without color portion of color i=1)

(46) TABLE-US-00001 04060 80 for which there is T(4). This concerns the pairings of the largest values. This leads to the values z(1).sup.i , z(2).sup.i , z(3).sup.i 04060 80 22,763 19,558 6,670

(47) This is the basis. The influence of the color component FA=q(1)=20 is now determined.

(48) To determine the influence of q(1), the combination of values with q(1)=FA

(49) TABLE-US-00002 20060 80 is chosen, for which T(3) exists. This leads to the values z(1).sup.1 , z(2).sup.1 , z(3).sup.1 (color data set Z1) 20060 80 22,759 29,779 5,153

(50) Then the combination of values is chosen where q(1)=0, the others equal, so

(51) TABLE-US-00003 0060 80 for which there is the T(5). This leads to the values z(1).sup.2 , z(2).sup.2 , z(3).sup.2 (color data set Z2) 0060 80 42,435 31,883 6,821

(52) The ratios V.sup.i of the two series of values to each other are formed:

(53) TABLE-US-00004 0,701 0,714 0,755

(54) These factors V.sup.i are now applied during the transformation. Thus from the base

(55) TABLE-US-00005 04060 80 22,763 19,558 6,670

(56) by multiplying the result of the searched z(1), z(2), z(3) with the factors

(57) TABLE-US-00006 204060 80 15,948 13,961 5,039.

(58) The invention describes a solution that is practicable and feasible for the person skilled in the art, with which a sufficiently fast and high-quality color space transformation into the color space of the concrete printing system is possible even with a very high resolution of a layout and a large number of input colors.

BRIEF DESCRIPTION OF THE DRAWINGS

(59) Further advantages and features result from the following description based on the figures. Thereby show:

(60) TABLE-US-00007 FIG. 1 a flow chart explaining the process steps. FIG. 2 A flowchart for estimating multiple missing colors. FIG. 3 the occurrence of more than 4-dimensional color data.

(61) According to FIG. 1, there is an input combination KB of color data 101 with color components Q={q(1), q(2), . . . , q(n)} from the source color space with n colors, which is to be transformed into the target color space with combinations of m values. The non-vanishing color components of this combination form a so-called color group. In step 102, a color i is searched for from this color group, whose color component is thus FA=q(i)>0, and for which certain conditions apply: 1) for the subset Q.sup.i (103) of the color data 101, for which the color component q(i).sup.i=0 is set, an output Z.sup.i (107) from the target color space must be assigned by the transformation rule TRV 106, which thus describes the transformation result of a color group without the color i, which is to be supplemented by the influence of the color i later. 2) There must exist another input Q1 (104) for which q(i).sup.1=FA, and which is otherwise arbitrary, to which an output Z1 (108) is assigned by the transformation rule TRV 106, i.e. which describes the transformation result of this other input with the same color component FA of the color i. 3) Appropriately, an input Q2 (105) is formed that is identical to Q1 except for the portion of color i that is q(i).sup.2=0. An output Z2 (109) is assigned to this input by the transformation rule TRV 106, thus describing the transformation result of this other input without the influence of color i.

(62) If this color i exists, the influence of its color component FA is now estimated from the ratio V.sup.i (110) of the output pair Z1 and Z2 with and without color component FA. This influence can be applied to all combinations with color share q(i)=FA for which there is an assignment without FA, in particular, of course, to the input combination KB. For this purpose, in step 111 the output Z.sup.i without the contribution of color i is multiplied component-wise by the ratio V.sup.i (110). Thus the sought result 112 is formed, which is the estimate of the target color values for the entire color group input combination KB.

(63) In other words, the color group of the input combination is reduced in size by removing color i, under the condition that an output is assigned to this smaller color group, and then color i is added by estimation so that the original color group is complete again. According to the invention, this reduction can also be carried out several times, so that after n steps at the latest one arrives at the empty color group, the unprinted substrate, for which an assignment can be easily determined. From there, if necessary, each individual color can be added step by step until the complete color group is obtained, as shown in FIG. 2.

(64) According to FIG. 2, there is color data 201 from the source color space with n colors, which are to be transformed and represent the input. In step 202, a color group is searched for which target color data 203 are available in the transformation rule. This color group is a subset of the color data 201 and is to be added to the full set step by step, while also adding the target color data 203 to the full output. If in step 204 the current color group is already complete, the output 205 is ready. Otherwise, one of the still missing colors i is selected in step 206. For this one, a pair of two color data sets Q1 and Q2 is now selected, namely in step 207 a color data set Q1, which contains the given color portion FA=q(i) of color i, and for which a combination of the m values z(1).sup.1, z(2).sup.1, . . . , z(m).sup.1 of the target color space, which form the color data set Z1 (208), and in step 209 the color data set Q2, which contains the same color components as Q1 for all colors except color i, while the component of color i is equal to 0, and for which a combination of the m values z(1).sup.2, z(2).sup.2, . . . , z(m).sup.2 of the target color space is present, which form the color data set Z2 (210). Both selected data sets, the color group with proportion of i and the color group without proportion of i, are color data of the n colors of the source color space. In step 211, the ratios of the m values of the color data set Z1 (108) to the m values of the color data set Z2 (210) are calculated component-wise. These ratios V.sup.i are applied component-wise to the current output in step 212 as the estimated effect of color i, and color i is added to the current color group (213). This is repeated if necessary until the color group is complete and thus the result of transformation 205 is available.

(65) FIG. 3 illustrates the known occurrence of more than 4-color overprints, although the individual objects do not use more than 4 colors, in addition to the description on page 7. Shown is a stylized packaging design 201 with an image area 202 built up in 4 colors in CMYK and a logo area 203 with a spot color. The enlarged view 204 of the design shows that the contours of the CMYK image and spot color rectangle do not overlap, only abut. So there are no 5-color areas in the design. Only the so-called trapping 205 in print production, which is used as described to avoid register-related flashes, enlarges one of the contours and thus creates overprinting areas 206 of the spot color with CMYK, where 5 colors now appear simultaneously. Independently of this, halftoning with antialiasing 207 can also mix halftone dots from portions of the areas belonging to them, so that further 5-color pixels 208 with CMYK and spot color portions are created.

(66) The preceding examples can be repeated with similar success by substituting the generically or specifically described reactants and/or operating conditions of this invention for those used in the preceding examples.

(67) From the foregoing description, one skilled in the art can easily ascertain the essential characteristics of this invention and, without departing from the spirit and scope thereof, can make various changes and modifications of the invention to adapt it to various usages and conditions.